In the July 2007 issue, Consumer Reports examined the calorie content of two kinds of hot dogs: meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several different brands. The meat hot dogs averaged 111.7 calories, compared to 135.4 for the beef hot dogs. A test of the null hypothesis that there's no difference in mean calorie content yields a P-value of 0.124. Would a 95% confidence interval for μMeat −μBeef include 0? Explain.

Since we FAIL to reject the null hypothesis, then if we construct an interval of 95% of confidence, the 0 should be included, because on the test hypothesis we conclude that there would be no significant difference between the means of the two groups analyzed, and the results obtained on the hypothesis test needs to be consistent with the confidence interval.

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

[tex]\bar x_{meat}=111.7[/tex] represent the sample mean of calories for the meat hot dogs

[tex]\bar x_{beef}=135.4[/tex] represent the sample mean of calories for the beef hot dogs

The system of hypothesis on this case would be:

Null hypothesis: [tex]\mu_{meat}-\mu_{beef}=0[/tex]

Alternative hypothesis: [tex]\mu_{meat}-\mu_{beef}\neq 0[/tex]

On this case we have the p value obtained, after calculate the statistic and we got that [tex]p_v =0.124[/tex] if we select a 5% significance level [tex]\alpha=0.05[/tex] we see that [tex]p_v >\alpha[/tex] and on this case we can FAIL to rejec the null hypothesis, so there is not a significant difference between the mean of the two tpes of hot dogs analyzed at 5% of significance.

And since we FAIL to reject the null hypothesis, then if we construct an interval of 95% of confidence, the 0 should be included, because on the test hypothesis we conclude that there would be no significant difference between the means of the two groups analyzed, and the results obtained on the hypothesis test needs to be consistent with the confidence interval.